The relationship between Stress-Energy tensor and Mass

[ShayanJ]

In Einstein field equations,the term that is responsible for curving Space-Time is the Stress-Energy tensor.But we know that mass should be able to curve space-time.So I think every mass distribution should have a Stress-Energy tensor associated with it.
What is that relationship?
Thanks

 

[dextercioby]

Volumic mass density is the 00 component of the stress-energy tensor.

 

[stevendaryl]

In Einstein field equations,the term that is responsible for curving Space-Time is the Stress-Energy tensor.But we know that mass should be able to curve space-time.So I think every mass distribution should have a Stress-Energy tensor associated with it.
What is that relationship?
Thanks

The relationship is explained in Wikipedia here: http://en.wikipedia.org/wiki/Stress–energy_tensor

The simplest case is a perfect fluid at rest. In that case, the nonzero components of the stress-energy tensor $T^{\alpha \beta}$ are:
$T^{0 0} = \rho$, where $rho$ is the mass-energy density, and
$T^{1 1} = T^{2 2} = T^{3 3} = p$, where $p$ is the pressure.

 

[K^2]

Volumic mass density is the 00 component of the stress-energy tensor.

Energy density, which is proportional to mass density only for a body at rest.

 

[ShayanJ]

Thanks guys
But what about other components?

 

[stevendaryl]

Thanks guys
But what about other components?

As I said, for a fluid at rest, the three spatial components of the stress-energy tensor are just the pressure.

 

[jtbell]

But what about other components?

The diagram on the Wikipedia page identifies what the various components (or groups of them) represent.

 

[cosmik debris]

Thanks guys
But what about other components?

In addition to what Steven said, the off diagonal terms are shear stresses.

 

[pervect]

And of course you have momentum density...if you have a moving object or fluid.